Realizability of tropical canonical divisors

<jats:p> We use recent results by Bainbridge–Chen–Gendron–Grushevsky–Möller on compactifications of strata of abelian differentials to give a comprehensive solution to the realizability problem for effective tropical canonical divisors in equicharacteristic zero. Given a pair <jats:inline-formula> <jats:tex-math>(\Gamma, D)</jats:tex-math> </jats:inline-formula> consisting of a stable tropical curve <jats:inline-formula> <jats:tex-math>\Gamma</jats:tex-math> </jats:inline-formula> and a divisor <jats:inline-formula> <jats:tex-math>D</jats:tex-math> </jats:inline-formula> in the canonical linear system on <jats:inline-formula> <jats:tex-math>\Gamma</jats:tex-math> </jats:inline-formula> , we give a purely combinatorial condition to decide whether there is a smooth curve <jats:inline-formula> <jats:tex-math>X</jats:tex-math> </jats:inline-formula> over a non-Archimedean field whose stable reduction has <jats:inline-formula> <jats:tex-math>\Gamma</jats:tex-math> </jats:inline-formula> as its dual tropical curve together with an effective canonical divisor <jats:inline-formula> <jats:tex-math>K_X</jats:tex-math> </jats:inline-formula> that specializes to <jats:inline-formula> <jats:tex-math>D</jats:tex-math> </jats:inline-formula> . </jats:p>